a grandfather purchased a brand new car in 1958 for ​$2500.the car depreciated ​$325 a year. what would the car be worth 4 years after it was​ bought?

Answer:

x = 4, y = -3

Step-by-step explanation:

{2x - y = 11

{x + 3y = -5

You can use the substitution method by solving for x in the second equation:

x + 3y = -5

Subtract 3y from both sides:

x = -3y - 5

Now, substitute this value for x into the first equation:

2x - y = 11

2(-3y - 5) - y = 11

Distribute:

-6y - 10 - y = 11

Add 10 to both sides:

-6y - y = 21

Combine like terms:

-7y = 21

Divide both sides by -7:

y = -3

Next, substitute this value for x into the second equation:

x + 3y = -5

x + 3(-3) = -5

Multiply:

x - 9 = -5

Add 9 to both sides:

x = 4

Answer:

(7, 3)

Step-by-step explanation:

2x - y =11                         2x-y =11

-2(x+3y)= (-5)-2              -2x-6y= 10

Then you will cross out the x, and add.

-7y =21 divide 7

y=-21/7 or y=3

Then you plug in the y where the y is and solve

2x-(3) = 11

2x = 14

x=7

Answer: 1 quarter, 1 dime and 1 nickel.

Step-by-step explanation:

Quarter: 25 cents.

Dime: 10 cents

Nickel: 5 cents

25 + 10 = 35

35 + 5 = 40

Answer: 25 (1 quarter), 10 (1 dime), 5 (1 nickel) is 0.40 cents when all three numbers are summed up.

Answer:

Step-by-step explanation:

Using Pythagoras Theorem, hypotenuse = 5

[tex]h = \sqrt{a^{2}+ b^{2}[/tex]

[tex]h = \sqrt{9+16 }\ = \sqrt{25}\ = 5[/tex]

sin x = height / hypotenuse = 3 / 5

cos y = base / hypotenuse = 3 / 5

sin x = cos y = 3 / 5

Answer:

13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

The area can be expressed as: [tex]\pi r^2+lw[/tex].

We have l=10, because 18-2(4)

We have w=8, as given.

Thus, the rectangle area is 80.

There are two semicircles, but they add to form a full circle, which makes things a lot easier. We have the circle area formula, and substituting the values gives us 50.24 as the circle volume

80+50.24=130.24.

Rounded to 1 decimal place that is 130.2

Hope this helps :)

Answer:

Amount at 15%=$2,411

Amount at 14%=$7,405

Step-by-step explanation:

let

x= the amount at 15% rate.

y=amount at 14% rate

y= x times 3 plus $172

y= 3x + $172 (1)

x times 15% plus y times 14% equals a return of $1,398.35 after one year

0.15x + 0.14y= $1,398.35 (2)

Recall,

y= 3x + $172

Substitute (1) into (2)

0.15x + 0.14y= $1,398.35

0.15x + 0.14(3x+172)=1398.35

0.15x + 0.42x + 24.08=1398.35

Collect like terms

0.15x + 0.42x=1398.35 - 24.08

0.57x=1374.27

Divide both sides by 0.57

x=2,411

x=$2,411

Find y

y= 3x + $172

=3(2,411) + 172

=7,233+172

=7,405

y=$7,405

Amount at 15%=$2,411

Amount at 14%=$7,405

Check:

$2,411*0.15=$361.65

$7,405*0.14=$1036.70

Total=$361.65 + $1036.70

=$1,398.35

Answer: A, B and, C are incorrect, what is D?

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

We can use ratios to solve

10 hours           x hours

-------------- = -------------

15 logs            9 logs

Using cross products

90 = 15x

Divide by 15

90/15 = 15x/15

6 = x

6 hours

Answer:

Below

Step-by-step explanation:

Jovie has maintained the fire burning with 15 logs for 10 hours.

● 15 => 10

Let's find how many hours do 9 logs keep the fire burning.

Let x be that time

● 9 => x

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 15 => 10

● 9 => x

● 15 * x = 9×10

● 15x = 90

● x = 90/15

● x = 6

So the time that the fire will keep burning is 6 hours.

Answer:

the probability if that is what you are asking for is 1/3 of winning a prize

Step-by-step explanation:

Answer:

1/3 chance per each person of winning a prize

Step-by-step explanation:

*the table being referred to is attached below

Answer:

The table does not show a proportional relationship between variable g and h.

Step-by-step explanation:

For a proportional relationship to exist between two variables, there must be a constant, of which serves like a unit rate, when comparing two variables.

Thus, in the table attached below, there is no obvious constant of proportionality between variable g and variable h.

Thus, [tex] \frac{9}{3} [/tex] ≠ [tex] \frac{36}{6} [/tex] ≠ [tex] \frac{81}{9} [/tex]

Answer: see proofs below

Step-by-step explanation:

Proofs are like a puzzle that you have to unravel.

You can manipulate the left side to get the right side (LHS → RHS)

                                                or

You can manipulate the right side to get the left side (RHS → LHS)

You will need to use Pythagorean Identities, Sum and Difference Identities, and/or Double Angle Identities when manipulating one of the sides.

Use the following Identities:

cos 2A = cos²A - sin²A

sin 2A = 2 cosA · sinA    Note that A can be substituted with 2A        

sin 3A = 3 sinA - 4sin³A

cos 3A = 4cos³A - 3cosA

***********************************************************************************

e) Prove: 4 sin A · cos³A - 4 cos A · sin³A = sin(4A)

LHS → RHS

Given:         4 sin A · cos³A - 4 cos A · sin³A

Factor:        4 sin A · cos x (cos²A - sin²A)

                  2(2 sin A · cos A)(cos²A - sin²A)

Double Angle Identity:  2(sin 2·A)(cos 2·A)

                                       2 sin (2A) · cos (2A)

Double Angle Identity:  sin (2·2A)

                                       sin 4A

Proven:  sin 4A = sin 4A   [tex]\checkmark[/tex]

*****************************************************************************************

f) Prove: 4 sin³A · cos 3A + 4 cos³A · sin 3A = 3 sin(4A)

LHS → RHS

Given:          4 sin³A · cos 3A + 4 cos³A · sin 3A

Triple Angle Identity:   4sin³A (4cos³A - 3 cosA) + 4cos³A (3sinA - 4sin³A)

Expand:      16sin³A · cos³A - 12sin³A · cosA + 12cos³A · sinA - 16sin³A · cos³A

Simplify:      12cos³A · sinA - 12sin³A · cosA

Expand:        6cos²A(2cosA · sinA) - 6sin²A(2cosA · sinA)

Double Angle Identity: 6cos²A(sin 2A) - 6sin²A(sin 2A)

Factor:       6sin 2A (cos²A - sin²A)

Double Angle Identity:  6sin 2A (cos 2A)

                                       3(2sin 2A · cos 2A)

Simplify:     3sin (2·2A)

                  3 sin 4A

Proven: 3sin 4A = 3sin4A   [tex]\checkmark[/tex]

Answer:

2/5 [tex]cm^2[/tex]

Step-by-step explanation:

To find the area of a rectangle do A = bh

When you substitute 4/6 for base and 3/5 for height  it will be A = 4/6 x 3/5

This means the area is 2/5

Answer:

2/5 cm^2

Step-by-step explanation:

The area of a rectangle is found by

A = l*w

A = 4/6 * 3/5

  Rewriting

  =4/5 * 3/6

   = 4/5 *1/2

  = 2/5 cm^2

Answer: Rises to the left and falls to the right

Step-by-step explanation:

Use the degree and the leading coefficient to determine the behavior.

There is a good video called "Describing End Behavior Using Limit Notation" by Mario's Math Tutoring, and it helps to show you how to find the end behavior with limits.

Answer: The same number of tickets was sold on the fourth day and tenth day.

Step-by-step explanation:

Given, T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was  released.

The average rate of change in a function with respect to the independent variable gives the value of change in a particular period.

If average rate of change in T(d) for the interval d = 4 and d = 10 is  is 0 , that means nothing has been changed in the number of tickets sold on 4th day and 10th day after the film release.

Hence, the correct statement is "The same number of tickets was sold on the fourth day and tenth day."

The correct option is (A).The same number of tickets was sold on the fourth day and tenth day.

Given,

T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released.

The Average rate of change in T(d) for the interval  d = 4 and d = 10 is 0.

We have to find which statement is true.

Since the average rate of change in T(d) for the interval d = 4 and d = 10 is 0, it means nothing has been changed in the number of tickets sold on day 4 and day 10 after the film release.

Hence, the correct statement is The same number of tickets was sold on the fourth day and tenth day.

Thus The correct option is A.

For more details follow the link:

https://brainly.com/question/8011401

Answer:

80

Step-by-step explanation:

0,   3,   8,   15,   24,  35,   48,   63,  80 which is the nth term

first step you have to find how many steps the sequence was going with.

examples= from 0 to 3 the steps were 3

                =from 3 to 8 the steps were 5

                = from 8 to 15 the steps were 7

you will recognize that the steps the sequence is going with is odd numbers.

so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.

Answer:

80

Step-by-step explanation:

Answer:

x = -15

Step-by-step explanation:

x - 15 = -30

add 15 to both sides

x = -15

Answer: C) 16

Step-by-step explanation:

A Hexagon has 6 Sides and Since the perimeter is 24, each side has a length of 4.

4 * 4 = 16

Answer:

21.5

Step-by-step explanation:

h(t) = -16t^2 + 35t + 5,

Let t = 1.5

h(1.5) = -16 (1.5)^2 + 35(1.5) + 5

        =-16 *2.25 +52.5+5

      = -36+57.5

      = 21.5

Answer: B

Step-by-step explanation:

Any inscribed quadrilateral (quadrilateral in a circle) has opposite angles that add up to 180 degrees.

So looking at he picture we can see that, (x+16) + (6x-4) = 180.

So your answer is B.

Answer:

Hey There!! The answer to this is B: angle P + angle R = 180

angle O + angle Q = 180

Here, they are only interested in R, therefore the first equation will be enough to solve for R.

angle P + angle R = 180

y + (3y + 8) = 180

We need to solve for y, so put that y value in (3y + 8) to find angle R.

y + (3y + 8) = 180

y + 3y + 8 = 180

We add the y terms: 4y + 8 = 180

Subtract 8 from both sides: 4y = 180-8 = 172

Divide both sides by 4

y = 172/4 = 43

Angle R = 3y + 8

Put y = 43 and calculate R.

R = 3(43) + 8

R = 137

Therefore, the measure of angle R is B:

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

B. 13.8

Step-by-step explanation:

The five-number summary consists of five items which is usually displayed on a box plot, and can be represented in ascending order.

The five-number summary given: 3.5, 12, 19.1, 25.8, 31.8, represents the following in ascending order:

1. The minimum value = 3.5

2. First quartile (Q1) = 12

3. The median = 19.1

4. Third quartile (Q3) = 25.8

5. The maximum value = 31.8

The interquartile range = Q3 - Q1

Therefore, the interquartile range of the data = 25.8 - 12 = 13.8

Answer: please find the answer in the explanation.

Step-by-step explanation:

1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.

2.) A person running down a field to score a touchdown. Not enough information.

3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.

4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.

5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.

6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.

Answer:

Side DA

Step-by-step explanation:

The point A has coordinates of (-2,6) and the point D has coordinates of (-2,-4). Since both points have the same x-coordinate, we can subtract point A's y-coordinate from point D's y-coordinate.

6 - ( -4) = 10 (Basically adding 4 to six since the 2 minus signs make a plus sign)

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

The side of the quadrilateral ABCD has a length equal to 10 is AD.

Distance is the amount of space between two points. The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The coordinate of vertex A = (-2, 6) while for D is D(-2, -4). Hence:

[tex]AD=\sqrt{(-4-6)^2+(-2-(-2))^2}=10\ units[/tex]

The side of the quadrilateral ABCD has a length equal to 10 is AD.

Find out more on distance at: https://brainly.com/question/17273444

Answer:

Step-by-step explanation:

According to the choices given, only statements 1 and 3 are correct!

The true statement about the shaded triangles is; ΔNXO is the result of rotating ΔPXM 180° clockwise about point X.

The correct statement about the shaded triangles to explain the congruency is;

ΔNXO is the result of rotating ΔPXM 180° clockwise about point X.

This is because when we rotate ΔPXM 180° clockwise about point X, the corresponding parts of both triangles will be congruent based on Congruency proofs.

Read more about Congruent shapes at; https://brainly.com/question/1675117

#SPJ2

Answer:

m² + 9n² + 4m - 12n - 6mn + 4

Step-by-step explanation:

18b

(2+m-3n)² = (2+m-3n)(2+m-3n)

= 2*2 + 2*m + 2*-3n + m*2 + m*m + m*-3n - 3n*2 -3n*m - 3n*-3n

= 4 + 2m - 6n + 2m + m² - 3mn - 6n  - 3mn + 9n²

= m² + 9n² + 2m + 2m  - 6n - 6n - 3mn - 3mn + 4

= m² + 9n² + 4m - 12n - 6mn + 4

Answer:

(2+m-3n)(2+m-3n)

Step-by-step explanation:

Here's solution:

(2+m-3n)(2+m-3n)

4 + 2m - 6n + 2m + m^2 - 3mn - 6n - 3mn + 9n^2

4 + 4m - 12n + m^2 - 9mn + 9n^2

I hope this is right, I'm a bit tired.

Hope this helps, and have a good day :)!

Answer: -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

[tex]4 \sqrt{6}[/tex]

Step-by-step explanation:

The question is not properly presented and has mission options; however, the solution is as follows

Given

[tex]\sqrt{96}[/tex]

Required

Simplify

[tex]\sqrt{96}[/tex]

Start by expanding

[tex]\sqrt{16 * 6}[/tex]

The expression can be split to:

[tex]\sqrt{16} * \sqrt{6}[/tex]

Take positive square root of 16

[tex]4 * \sqrt{6}[/tex]

[tex]4 \sqrt{6}[/tex]

The expression cannot be further simplified

we need a picture of the weather data